AlllOb 'I ?'’ 320

NBS

PUBLICATIONS

NBSIR 83-2635

A Computer Algorithm for

Estimating infiltration and

Inter-Room Air Flows

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Building Physics Division

Washington. DC 20234

IMovemoer 1 S82

Issued Fecruarv 1383

f-tiG

ii160

.1)56

63-2635

1963

Sponsored bv

National Bureau of Standards

and

Building Energy Sciences Br-mch

Office of Building Energy Research and Development

t.S. Department o* Energy

Lashing ton, DC 20545

national bureau

OF STANDARDS

lierary

MAR 1 l 1983

NBSIR 83-2635

A COMPUTER ALGORITHM FOR

ESTIMATING INFILTRATION AND

INTER-ROOM AIR FLOWS

George N. Walton

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Building Physics Division

Washington, DC 20234

November 1 982

Issued February 1983

Sponsored by

National Bureau of Standards

and

Building Energy Sciences Branch

Office of Building Energy Research and Development

U.S. Department of Energy

Washington, DC 20545

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

ABSTRACT

This report discusses the extension of an infiltration predicting technique to

the prediction of inter-room air movements. The air flow through openings is

computed from the ASHRAE crack method together with a mass balance in each

room. Simultaneous solution of the mass balances in all rooms having both

large and small openings is accomplished by a slightly modified Newton's method.

A simple theory for two-way flow through large openings is developed from con- sideration of density differences caused by different temperatures in adjoining

rooms. The technique is verified by comparison to published experimental

results. The results indicate that the simple model provides reasonable results

for complex two way flows through openings. The model is as accurate as the

available data, that is, about +20%. The air flow algorithm allows infiltration

and forced air flows to interact with the doorway flows to provide a more general

simulation capability.

Key wordsbuilding energy analysis; building heat transfer; computer modeling;

convection; infiltration; ventilation.
PREFACE

This report is one of a series documenting MBS research and analysis efforts in

developing energy and cost data to support the Department of Energy/National

Bureau of Standards Measurements Program. It was prepared by the Thermal Analysis Group, Building Physics Division, Center for Building Technology, National

Engineering Laboratory, National Bureau of Standards (NBS). This work was jointly sponsored by (NBS). The development of multi-room air flow modeling

was supported by DoE/NBS Task Order A008 under Interagency Agreement No. E-77-

A-01-6010. This report describes a computer program which was written as part

of an effort to develop a comprehensive modeling technique for predicting the

simultaneous transfer of air, moisture, and heat in and through multi-room

buildings

The author wishes to acknowledge the support and direction given by

Dr. T. Kusuda, Thermal Analysis Group Leader.

iv
TABLE OF CONTENTS

Page

ABSTRACT iii

PREFACE iv

1. INTRODUCTION 1 1.1 BACKGROUND 1 1.2 OBJECTIVES

1.3 SCOPE

2. CALCULATION METHODS 3

2.1 THE AIR FLOW EQUATION 3

2.2 SOLUTION OF THE FLOW EQUATIONS 3

2.3 A THEORY OF FLOW THROUGH LARGE OPENINGS 6

3. VALIDATION OF THE LARGE OPENING MODEL 8

3.1 FLOW THROUGH OPENINGS IN VERTICAL PARTITIONS 8

3.2 FLOW THROUGH OPENINGS IN HORIZONTAL PARTITIONS 8

4. CONCLUSIONS AND RECOMMENDATIONS 10

5. REFERENCES 11

FIGURES 12

APPENDIS A: LISTING OF THE AIR FLOW TEST PROGRAM 17

APPENDIX B: SAMPLE INPUT FOR THE AIR FLOW TEST PROGRAM 27
LIST OF FIGURES

Page

Figure 1. Orifice Flow Meter Coefficients 12

Figure 2. Schematic of opening in a vertical partition 13

Figure 3. Two-room model for determining natural convection

transfer through the doorway 1A

Figure A. Comparison of experimental results for convection

through openings in vertical partitions 15

Figure 5. Experimental results for air flow through a square

opening in a horizontal partition 16
1

INTRODUCTION

1 . 1 BACKGROUND

Although numerous building thermal modeling techniques and computer programs

,

for example NBSLD [1], BLAST [2], and DOE-2 [3], exist throughout the United

States, none of the existing techniques /'programs handle the following processes

simultaneously:

- envelope heat transfer

- envelope air leakage

- envelope solar heat gain

- room-to-room heat transfer

- room-to-room air and moisture transfer

- intra-room air movement

- energy consumption by the heating/cooling equipment

- indoor comfort

- water vapor condensation and contaminant migration.

Existing models are virtually all single-room models where dynamic coupling

between the heated and non-heated spaces and/or the cooled and non-cooled

spaces are ignored.

Comprehensive multi-room building simulation capabilities will be needed in

the coming years for the following reasons:

1. Intra-room convection plays a significant role not only for the transfer

of heat from the interior surfaces to the room air but also for the thermal

comfort of the occupants. Yet existing computational technology for predicting the room temperature stratification and room air motion is very

inadequate

2. Passive solar design techniques are expected to be used to a large extent

in new building design. Proper design is going to depend on understanding

and being able to predict natural energy flows within the buildings.

3. Proper control of the air flow in the central air system requires accurate

knowledge of room-by-room energy demand.

4. Moisture and contaminant distribution throughout a building must be capable

of being predicted in order to insure adequate designs as the emphasis on "tighter" buildings increases.

5. Until such capability exists, effective design of internal partitioning

with respect to natural ventilation can only be done by empirical techniques.

In response to these needs, a research-oriented computer program has been

developed to allow the detailed study of simultaneous air, heat, and moisture

transfer in and through a building with complex internal architecture. This

program is called the Thermal Analysis Research Program (TARP). Documentation

[4] for the program will soon be published. Primary emphasis in the develooment

1
of TARP has been on air transfer because this is a major shortcoming of present

techniques and because it is basic to further developments in moisture and

contaminant analysis. A previous report [5] describes initial results in the

development of TARP and listed five significant areas for further research:

1. Calculation of air flows through large openings in reasonable

computation time,

2. Calculation of two-way flows between rooms,

3. Accurate evaluation of the wind induced pressure distribution around

the envelope of the building,

4. Calculation of the effects of room air stratification, and

5. Availability of data for estimating the opening areas in the envelopes

of buildings.

This report will address the first two areas.

1.2 OBJECTIVE

The overall objective of this research effort is to develop a comprehensive

modeling technique for predicting simultaneous transfer of air, moisture, and

heat in and through multi-room buildings. The objective of this particular

study is the development of a method for predicting air flows through large

openings between rooms.

1.3 SCOPE

Section 2 of this report discusses the extension of an infiltration predicting

technique to the prediction of inter-room air movements. The technique is verified by comparison to published experimental results in section 3. Conclusions

and recommendations are given in section 4.

2
2. CALCULATION METHODS

2.1 THE AIR FLOW EQUATION

The TARP air flow algorithm is described in detail in reference [5] where the

program was called the Multi-Room Loads Program (MRLP). The air flow algorithm

is based on the equation [6]

F = K * (AP) X

(1)

where

F = flow rate (kg/s)

K = a constant

AP = pressure difference across an opening (Pa)

X = flow exponent

Pressure differences arise from wind, air density differences, and system

induced flows. By applying equation (1) to all openings in the building

envelope and all openings between rooms and requiring a mass balance in each

room, a set of simultaneous non-linear algebraic equations is created which

can be solved for the zone pressures and the air flow through each opening.

An estimate for the value of K was made by referring to the orifice equation:

F=C*A*p* / 2 * AP / p (2)

where

C = flow coefficient

A = observed opening area (nP)

p = air density (kg/m^)

When the opening is small, C equals 0.6 for a wide range of Reynolds numbers

as shown in figure 1 [7], TARP assumes this value of C as a default. TARP

allows a variable flow exponent (instead of the 0.5 of the orifice equation)

because building presurization measurements typically correlate to equation

(1) when X equals about 0.65 [5].

2.2 SOLUTION OF THE FLOW EQUATIONS

The development of a solution technique for the air flow equations has been

particularly troublesome. Efforts have focused on two techniques which are described by Conte and DeBoor [8]. The first technique is the classic Newton's

method. The mass balance requirement may be expressed as

l V± = 0 (3)

for every room. The flows, Fj_ , are summed over all openings, i, in the enclosing

surfaces of the room. In Newton's method, successive values of room pressure,

P n , for each room, n, are calculated by

3
(4)

(k+1) (k) _

where k is the iteration number and C is computed from the matrix relationship

I J ] * [ C ] - [ B ] (5)

where [ B ] is a column matrix each element given by

B n = Z F

± (6)

and J is the square (i.e., N by N for a building of N rooms) Jacobian matrix.

The values of the diagonal elements of the Jacobian matrix are given by

Jn n

Zi

3Fi

3P n

(7)

for all openings, i, into room n. The values of the other elements are given

by

Jn , m

Zi

( 8 )

for all openings, i, between room m and room n. Iteration proceeds until the

net air flow into every room, B n , is sufficiently close to zero. These partial

derivatives are very easy to compute

3F • —- = X, * F • / AP (9)

8Pn

1 1

d¥—±

= X, * F,/AP

3Pmm

or

3F • 3P

1 = 0

m

(inter-room surface) (10)

(envelope surface) (11)

Note that the term (AP)‘^ ^ has been eliminated from these expressions, thus

allowing evaluation of the derivatives by a simple division rather than a time

consuming exponential. Also note that as AP approaches zero, the derivative

is undefined.

The second method calls for successively approximating each room pressure

according to

4
p ( 12 )

( k+l)

= p

(k) _ zy /T. —

n n 1 3Pn

where k is again the iteration number. This method is quite simple and requires

less storage space than Newton’s method because it does not use the Jacobian

matrix.

Initial tests of these two methods showed that, although Newton’s method was fastest for most test cases, it occasionally would not converge. The second

method converged for the original test cases and was chosen for the initial

version of TARP [5], It was then found that this method converged very slowly

when the openings between rooms were much larger than the openings in the

building envelope which is a very common condition. This problem led to a re- examination of the Newton's method. A simple four room test case was found to

usually be quadratically convergent (about 4 iterations) except for a few cases where it converged verly slowly (about 30 iterations). In those cases it was found that successive iterations were over-correcting. That is, they were suc- cessively far above and then far below the correct solution because successive

corrections were of about the same magnitude but opposite sign. Convergence

could be achieved by reducing the size of the pressure correction by about one

half. Since the Newton's method is normally rapidly convergent, it is also

necessary to reduce the size of the correction only when over-correcting occurs.

The reason for occasional slow convergence of the Newton’s method has not been

found. It can occur with nothing more than a change in wind direction from

what was a quardratically convergent case. It often occurs when the wind and

stack pressures are about equal. Convergence is always fastest when the flow

exponent for inter-room openings is near one. The experimental studies below

indicate, however, that the exponent should be one half.

The air flow algorithm was incorporated into a test program which allowed

various solution techniques to be studied without revising TARP, which is very

large. A listing of the test program is attached as appendix A. Details of

the solution algorithm are discussed in that listing.

The Newton's method requires the simultaneous solution of matrix equation (5)

at each iteration. Several techniques were considered for that solution. The

first choice, and the one ultimately chosen, was Gauss elimination. It has the

disadvantage that solution time is proportional to the cube of the number of

equations, N, when N is large. The number of equations is equal to the number

of rooms. The Cholesky method [9] is somewhat faster at large N, but is was found to be sensitive to computer truncation errors. A Gauss-Seidel iteration

was also tried since it has solution time proportional to the square of N.

However, this iteration also failed for large openings in much the same way

that equation (12) did. The Newton's method was tested for larger numbers of rooms. It was found that the number of iterations increased with the number of rooms. Thus, many room require both longer iterations and more iterations.

The number of iterations was also found to increase with the size of the interroom openings, but it did not increase as dramatically as it had done with

equation (12). Therefore, the Newton's method is most appropriate for a small

5
number of rooms with large execution time penalties paid for simultaneously

solving many rooms.

TARP uses an hourly heat balance in estimating dynamic room energy requirements.

This heat balance is solved iteratively, and at each iteration a quasi-steady

solution of the air flow equations is obtained by the Newton's mehtod described

above. Techniques used to reduce the number of heat balance iterations

contribute to the overall efficiency of TARP and are described in [5].

2.3 A THEORY OF FLOW THROUGH LARGE OPENINGS

Equation (1) permits air to flow only one direction through an opening. Large

openings, such as doorways, may have two way flow as the stack effect between

two rooms may cause a positive AP at the bottom of the doorway and a negative

AP at the top (or vice versa). A theoretical estimate of the stack induced air

flow through a large opening in a vertical partition (a doorway) is given by

Brown and Solvason [9]. The following discussion shows that the TARP method is

equivalent. Figure 2 shows a cross section of a rectangular opening of height

H and width W in a vertical partition which separates two rooms at temperatures

Tt and T^. The absolute pressure at the centerline (z = 0) is everywhere equal.

The pressure difference caused by stack effect at height z is

p

l " p

2 = (Pi - P 2

) * g

* z (13)

The volumetric flow through an infinitesimal area is given by

dQ = C * W * dz * / 2 * Ap /p (14)

which can be integrated to give the flow through the top half of the opening

Z=H/2

Q = / dQ = C/3 * W * / g

* Ap/p * H3 (15)

Z=0

The coefficient of thermal expansion is p = -Ap/(p * AT) where p is the average

density. For computational simplicity TARP uses the density of the incoming

fluid instead, but this cannot cause a significant error at normal temperatures.

Other definitions are:

heat transfer rate: q = Q*p*c* (Tj_ - T^) (16a)

heat transfer coefficient: h = q / [W * H * (T^ - T2 )] (16b)

Nusselt number: Nu = h * H / k (I6c)

Prandtl number: Pr = c * u /k (16d)

Grashof number: Gr = p“*g*|9*(T^-T2 )*H^/u (16e)

The expressions can be substituted into equation (15) to give

6
Nu = C/3 * Pr * / Gr (17)

This simplified analysis has neglected viscous effects and effects of an air

velocity parallel to the partition. According to Brown and Solvason the viscous

effects reduce the air flow through thick partitions and an air velocity may

either increase or reduce the air flow.

TARP can handle the two-way air flow through a doorway by dividing the door

into an upper and a lower opening. It is easy to determine the heights of the

two openings which cause a stack effect giving the same volumetric flow as the

Brown and Solvason model. These turn out to be 13/18 * H for the upper opening

and 5/18 * H for the lower one.

Brown also studied openings in horizontal partitions [10]. He developed a theoretical expression for convection through such openings:

Nu = (0.29 to 0.35) * Pr * f~Gr (18)

In this case the Nusselt and Grashof numbers are based on the thickness of the

partition. This thickness is the vertical space available for the development

of a stack effect.

7
3. VALIDATION OF THE LARGE OPENING MODEL

3.1 FLOW THROUGH OPENINGS IN VERTICAL PARTITIONS

Weber and Kearney [11] give a correlation for the two way flow through a doorway

based on temperature measurements in the doorway

Nu = 0.26 * Pr * / Gr (19)

and another based on average room temperatures

Nu = 0.3 * Pr * / Gr ( 20 )

These correlations are based on similitude experimental studies of the room shown in figure 3 and tests on a full scale structure with a similar configuration. Weber and Kearney estimated that they should be dependable to within 20

percent. They also compare their results to two other studies (figure 4)

including Brown and Solvason's. Comparing equations (19) and (17) gives a value of 0.78 for the flow coefficient, C. Equation (20), which uses average room temperatures, gives a value of 0.90 for the flow coefficient. This seems unreasonably large and is apparently due to the uneven temperature distributions which occur in real rooms, especially above the door openings. A study

of a dorrway between a small room and a much larger, high heat loss, two-story

room did not agree well with the correlation (20).

The TARP model dividing the doorway into halves was used for a wide range of

parameters and the results compared to equation (19). The inter-room mass and

energy flows were computed for five values of AT (2, 4, 6, 8, and 10 C) each

at five doorway heights (1.0, 1.5, 2.0, 2.5, and 3.0 meters). A flow coefficient of .78, a flow exponent of 0.5, and stack heights at 5/18ths and 13/l8ths

of the doorway height give TARP computed mass and energy flows which agree with

equation (19) to within 0.1 percent for all cases.

3.2 FLOW THROUGH OPENINGS IN HORIZONTAL PARTITIONS

Figure 5 shows the experimental results (H = thickness; L = width of square

opening) of Brown's study of openings in horizontal openings [10]. In this

configuration there is a significant frictional effect in the thicker

partitions. Brown incorporated this into a single equation:

For a TARP evaluation it is better to to consider the thickness effect as a modifier to the stack height. A TARP model of an opening in a horizontal

partition would again divide it into two openings, one a distance Z above the

center of the partition and one and equal distance below it. Then, for C = 0.78, the values of Z for different H/L would be:

Nu = 0.0546 * pr * Gr- 55 * (L/H)* 33

( 21 )

8
H/L Z

0833 . 168*H

167 . 120*H

333 . 093*H

667 .074*H

These almost exactly duplicate the Brown results.

There are still several questions about this model. The effects beyond the

studied ranges of Gr and H/L are not known. The model predicts that the flow

should go to zero as H approaches zero! There should be some flow. It is

possible that two separate openings would behave differently than a single

opening of equivalent area because one-way flow could develop in each. These

questions indicate room for further experimental work. In addition, a TARP

model would have to allow for no flow between rooms when the upper is warmer

than the lower.

9
4. CONCLUSIONS AND RECOMMENDATIONS

The results indicate that the simple TARP model provides reasonable results for

complex two way flows through openings. The model is as accurate as the available data, that is, about +20 percent. The TARP air flow algorithm allows

infiltration and forced air flows to interact with the doorway flows to provide

a more general simulation capability. Although more work must be done for other

building configurations, the close match between the TARP algorithm and the

experimental correlations is encouraging.

Because of the rapid increase of calculation time with the number of rooms simulated, it is recommended that large buildings with many rooms be simulated

by dividing the building into groups of closely coupled rooms. First, treat

each group of rooms as a single room to solve for the infiltration through the

building envelope and air flows between the groups of rooms. Then, while treating those air flows as constant gains or losses to the appropriate rooms, solve

for the air flows between the individual rooms in each group.

Further study is needed on the simulation of room air stratification both for

its direct effects on comfort and energy requirements as well as for its effect

on inter-room air movement. Study is also needed on the calculation of the

wind pressure on the building envelope. Then detailed validation should be performed with carefully selected full scale tests. After successful validation,

it will still be necessary to develop air openings data for typical construction

components and building techniques for the analysis and design of buildings.

10
5 REFERENCES

[1] Kusuda, T. , "NBSLD, the Computer Program for Heating and Cooling Loads

in Buildings," NBS Building Science Series 69, July 1976.

[2] Hittle, D. C. , "The Building Loads Analysis and Systems Thermodynamics

(BLAST) Program, Version 2.0: Users Manual", U.S. Army Construction

Engineering Research Laboratory Report TR-E-153, June 1979.

[3] "DOE-2 Users Guide, Version 2.1", Lawrence Berkeley Laboratory Report

LBL-8698, May 1980.

[4] Walton, G. N. , "Thermal Analysis Reasearch Program Reference Manual",

National Bureau of Standards, in review.

[5] Walton, G. N. , "Calculation of Inter-Room Air Movement for Multi-Room

Building Energy Analysis", National Bureau of Standards Interagency

Report (NBSIR) 81-2404, November 1981.

[6] ASHRAE Handbook - 1977 Fundamentals, ASHARE, 1981, p. 21.4.

[7] ASHRAE Handbook - 1981 Fundamentals, ASHRAE, 1981, p. 4.13, Figure 18.

[8] Conte, S. D. and De Boor, C. , Elementary Numberical Analysis, an Algorithmic Approach, McGraw-Hill, 1972, pp. 84-88.

[9] Brown, W. G. , and Solvason, K. R. , "Natural Convection Through Rectangular

Openings in Partitions - 1: Vertical Partitions", Int. Journal of Heat

and Mass Transfer, Vol 5, 1962, pp. 859-867.

[10] Brown, W. G. , "Natural Convecton Through Rectangular Openings in

Partitions - 2: Horizontal Partitions", International Journal of Heat

and Mass Transfer, Vol 5, 1962, pp. 869-881.

[11] Weber, D. D. , and Kearney, R. J., "Natural Convective Heat Transfer

Through an Aperture in Passive Solar Heated Buildings”, 5th National

Passive Solar Conference, 1980, pp. 1037-1041.

[12] Weber, D. D. , "Similitude Modeling of Natural Convection Heat Transfer

Through an Aperture in Passive Solar Heated Buildings", Los Alamos

Scientific Laboratory Report LA-8385-T, June 1981, 114 p.

11
1

I 00

-}C90

*0l_CS N0M8EP =

Figure 1. Orifice flow ueter coefficients [6]
ROOM 1

Ti Pi

A Z = ‘ ROOM 2

>< +2 T 2 P

!

i -z

. Schematic of ooeninsr in a vertical oa
PARTITION

1 in. POLYSTYRENE COLO PLATE

Figure Two-room model for determining natural convection

transfer through the doorway [11]
Log(Nu

d

/Pr)

rizure Comparison of experimental results for convection

through openings in vertical partitions [12]
o

m

<r

<\J

o

©

u>

T

<r

(VI

4o

©

©

T

o

c o o O O O O O Q oo o o o o o c o n <r r

r

c 31 -0 f~* <£ T fO

= ->a'/^7 V

16

Figure

.6.

Experimental

results

for

air

flow

through

a

square

opening

in

a

horizontal

partition

[10]
APPENDIX A: LISTING OF AIR FLOW TEST PROGRAM

The subroutines and variables used in this program were prepared for easy

inclusion in TARP . Several features could have been simplified or improved if

the only goal had been to develop a stand-alone air flow analysis computer

program.

Descriptions of variables in common:

ACNVG1

ACNVG2

ACNVG3

AFSPTR

AIRDEN

AMAXIT

CPAIR

DIR

DTR

FAHS

FAREA

FAZM

FEXP

FRACT

HCOUNT

LIST

MAXAFS

MAXZON

MCPM

MCPTM

NAFS

NZON

OBP

ODB

PS

PW

PZ

SPD

SORTDZ

STDTIM

SUMAF

TZ

zs

ZT

ZZ

relative air flow convergence,

minimum air flow (kg/s),

minimum pressure difference (Pa).

air flow opening pointers (near side and far side room numbers).

ambient air density (kg/m^).

maximum air flow mass balance iterations.

specific heat of air (kWh/kg C).

wind direction (degrees).

conversion factor: degrees * DTR = radians,

air flow from the air handling system (m^/s).

effective flow area (ra-).

azimuth angle of surface (degrees),

air flow exponent.

fraction of computed correction (to speed convergence),

count of heat balance iterations.

printed output control flag (0 = least detail, 2 = most).

parameter: maximum number of air flow openings.

parameter: maximum number of zones. inward mass flow rate time specific heat (W/C)

inward energy flow of moving air (W)

number of air flow openings.

number of zones (rooms).

ambient barometric pressure (Pa).

ambient dry bulb temperature (C).

stack pressure (Pa)

wind pressure (Pa). zone (room) air pressures (Pa). [zone 0 = ambient]

wind speed (m/s)

square root of the zone air density (/kg/m^) . [zone 0 = ambient]

hour counter (standard time). sum of (unsigned) zone air flows (kg/s). zone air temperature (C). [zone 0 = ambient]

height of opening (m)

maximum height of surface(m).

height of zone (m) . [zone 0 = ambient]

Listing of subroutines:

The driver program, MAIN, is structured to test convergence for various

convergence limits and ambient conditions for a single building configuration.

Other driver programs were written to test air flows through openings for

17
comparison to the experimental results. This routine uses NAMELIST input for

the control variables. A sample input deck is shown in Appendix B.

12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

C

c

c

c

PROGRAM MAIN

COMMON /ENVT/ ODB( 1 ) ,0BP( 1 ) ,SPD( 1 ) ,DIR( 1 )

, AIRDEN, CPAIR, DTR, STDTIM,

LIST, HCOUNT, ACNVG1 , ACNVG2 , ACNVG3 , AMAXIT , FRACT , NAFS , NZON

INTEGER STDTIM, HCOUNT, AMAXIT, NAFS, NZON

REAL ODB , OBP , SPD , DIR, AIRDEN, CPAIR, DTR,

ACNVG1, ACNVG2 , ACNVG3 , FRACT

NAMELIST /CONTROL/ AMAXIT, ACNVG1 ,ACNVG2 ,ACNVG3 , ODB , OBP , SPD

,

DIR, LIST

CALL INITAIR

10 CONTINUE

READ CONTROL

IF(AMAXIT.LE.O) STOP ' END OF RUN*

PRINT CONTROL

CALL AIRMOV

GO TO 10

END

Subroutine INITAIR initializes most of the variables for the air flow simulation.

In particular, it includes the statements that read the user data for the zone (line 56) and opening (line 74) descriptions. Wind and stack pressures are set

to zero (lines 91, 92). Wind pressure (PW) remains zero for all inter-room

openings

.

12

3

4

56

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

C

C

C

c

c

c

c

SUBROUTINE INITAIR

REAL Z, T, F

INTEGER MAXAFS

PARAMETER (MAXAFS=128)

INTEGER MAXZ0N

PARAMETER (MAXZON=36)

COMMON /AFSL/ FAREA( MAXAFS ) ,FEXP( MAXAFS ) ,ZS( MAXAFS ) ,ZT( MAXAFS )

,

PW(MAXAFS) , PS (MAXAFS) , FAZM( MAXAFS) , AFSPTR( 2 , MAXAFS)

INTEGER AFSPTR

REAL FAREA, FEXP , ZS , PW, PS, FAZM, ZT

COMMON /ENVT/ 0DB( 1 ) ,OBP( 1 ), SPD( 1 ) ,DIR( 1 )

, AIRDEN, CPAIR, DTR, STDTIM,

LIST, HCOUNT,ACNVG1 ,ACNVG2 ,ACNVG3 , AMAXIT, FRACT, NAFS , NZON

INTEGER STDTIM, HCOUNT, AMAXIT, NAFS, NZON

REAL ODB, OBP, SPD, DIR, AIRDEN, CPAIR, DTR,

18
22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

ACNVG1

,

C

ACNVG2

,

ACNVG3

,

FRACT

COMMON / ZONL/ MCPM(MAXZON) ,MCPTM(MAXZON) ,TZ(0 jMAXZON)

,

ZZ ( 0 : MAXZON )

, SORTDZ ( 0 : MAXZON ) , PZ(0 : MAXZON)

,

FAHS ( MAXZON ), SUMAF (MAXZON)

REAL TZ, ZZ, SQRTDZ , PZ, FAHS, MCPM, MCPTM, SUMAF

C

C INITIALIZE VARIABLES.

HC0UNT=1

STDTIM=1

AMAXIT=20

FRACT=. 55

LIST-1

NAFS=0

NZON=0

DTR=0. 0174533

ACNVG1=. 0001

ACNVG2=. 000005

ACNVG3=. 00001

CPAIR=1004

ODB ( 1

) =0

0BP( 1 )=100000

SPD( 1 )=5

DIR( 1 )=270.

SQRT2=SQRT(2.0)

WRITE(*,101)

101

F0RMAT( ' 1

' ,8X, f N ' , 6X, f ZZ ' , 6X, ' TZ ' ,4X, ’FAHS’)

10 CONTINUE

C READ ZONE DATA:

C HEIGHT, TEMP, SYSTEM FLOW

READ *, Z , T,

IF (Z.LT.0.0) GO TO 20

NZON-NZON+l

WRITE(* , 102) NZON, Z , T,

102 FORMATC ZON: ’ ,I4,3F8.2)

ZZ(NZ0N)=Z

TZ (NZ0N)=T

FAHS ( NZON )=F

GO TO 10

20 CONTINUE

WRITE(* , 103)

103 FORMATC 'O' ,8X, *1 N M* ,7X, ' A’ ,7X, ’X' ,7X, 1 C’ ,5X, 'AZM'

,

- 6X, ’ZS’ ,6X, ’ZT’)

30 CONTINUE

G

C

C

C

READ *, N , M , A , X , C , AZ

IF (N.LE.O) GO TO 40

READ OPENING DATA:

NEAR SIDE ZONE, FAR SIDE ZONE,

AREA, EXPONENT, FLOW COEFFICIENT,

AZIMUTH, HEIGHT, SURFACE HEIGHT

Zi ,Z2

19
73 NAFS=NAFS+1

74 WRITE(*, 104) NAFS , N , M , A , X , C , AZ , Z 1 ,Z2

75 104 FORMATC AFS: ’ , 314 , 3F8 . 4 , 3F8 . 2)

76 AFSPTR(1 ,NAFS)=N

77 AFSPTR( 2 ,NAFS) =M

78 FAREA( NAFS ) =SQRT2* C*

A

79 FEXP(NAFS)=X

80 FAZM( NAFS )=AZ

81 ZS(NAFS)=Z1

82 ZT(NAFS)=Z2

83 GO TO 30

84 40 CONTINUE

85 C COMPUTE VARIABLES.

86 TZ(0)=ODB( 1

)

87 AIRDEN=0. 0034838*OBP( 1 )/ ( 0DB( 1 )+273 . 15)

88 ZZ(0)=0.0

89 PZ(0)=0.0

90 DO 50 1=1, NAFS

91 PS(I)=0.0

92 PW(I)=0.0

93 50 CONTINUE

94 RETURN

95 END

Subroutine AIRMOV computes the room air densities (lines 31-33), the wind and

stack pressures for each opening (lines 35-52), calls for solution of the mass balance (line 54), Computes the mass and enery flows into each room (lines

56-76), and reports the room and oppening air flows (lines 74-90).

Descriptions of local variables:

I index for openings.

N room number.

M adjacent room number (0 = ambient).

V wind speed modified for height (m/s).

W wind pressure at given height (Pa).

Y relative surface to wind direction (degrees).

X wind pressure direction modifier.

DP pressure difference across opening (Pa)

.

MCP mass flow rate times specific heat of air flow into room (W/ C)

.

20
12

3

4

5

6

78

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

SUBROUTINE AIRMOV

REAL MCP

INTEGER MAXAFS

PARAMETER (MAXAFS=128)

C

c

c

c

c

c

c

cc

10

c

c

INTEGER MAXZON

PARAMETER (MAXZ0N=36)

COMMON / AFSL/ FAREA(MAXAFS) ,FEXP (MAXAFS ) ,ZS (MAXAFS ) ,ZT(MAXAFS)

,

PW( MAXAFS) ,PS(MAXAFS) , FAZM( MAXAFS) ,AFSPTR( 2

, MAXAFS)

INTEGER AFSPTR

REAL FAREA, FEXP , ZS, PW, PS, FAZM, ZT

COMMON /ENVT/ ODB( 1 ) ,OBP( 1 ), SPD( 1 ) ,DIR( 1 ) ,AIRDEN, CPAIR,DTR, STDTIM,

LIST, HCOUNT , ACNVG1 ,ACNVG2 ,ACNVG3 ,AMAXIT, FRACT,NAFS ,NZON

INTEGER STDTIM, HCOUNT, AMAXIT, NAFS , NZON

REAL ODB , OBP , SPD , DIR, AIRDEN, CPAIR, DTR,

ACNVG1 , ACNVG2 , ACNVG3 , FRACT

COMMON / ZONL/ MCPM(MAXZON),MCPTM(MAXZON),TZ(0:MAXZON),

ZZ(0 : MAXZON) , SQRTDZ(0 :MAXZON) , PZ(0 : MAXZON)

,

FAHS (MAXZON ), SUMAF ( MAXZON

)

REAL TZ, ZZ, SORTDZ, PZ, FAHS, MCPM, MCPTM, SUMAF

COMPUTE ZONE AIR DENSITIES.

DO 10 N=0 ,NZON

SQRTDZ(N)=SQRT(0.0034838*OBP( STDTIM)/ (TZ(N)+273 . 15)

)

CONTINUE

COMPUTE CONSTANT DELTA-P.

DO 20 1=1, NAFS

N=AFSPTR( 1,1)

M=AFSPTR( 2,1)

IF(M.E0 . 0 .AND. HCOUNT. EQ.l) THEN

WIND PRESSURE.

V=SPD(STDTIM)*(0.1*ZT(I))**0. 143

W=0. 5*AIRDEN*V*V

Y=AMAX1 ( FAZM( I ) ,DIR( STDTIM) ) -AMIN 1 ( FAZM( I ) ,DIR( STDTIM)

)

IF(Y.GT. 180. ) Y=360. -Y

IF(Y.LE. 90 . ) X=0. 75-1. 05/90. *Y

IF(Y.GT. 90. ) X=0. 15/90. *Y-0. 45

PW(I)=X*W

END IF

STACK PRESSURE.

PS(I)=9.80*((ZZ(M)-ZS(I))*SQRTDZ(M)*SQRTDZ(M)-

(ZZ(N)-ZS(I))*SQRTDZ(N)*SQRTDZ(N))

IF( LIST. GE. 1 ) PRINT * ,

' CONSTS :

’ , I ,PS( I) , PW( I)

21
52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

C

20 CONTINUE

COMPUTE ZONE PRESSURES TO CONVERGENCE.

CALL SOLVZP

C COMPUTE ZONE FLOWS.

DO 30 N=l,NZON

MCPM(N)=0.0

MCPTM(N)=0.

0

30 CONTINUE

DO 40 1=1 ,NAFS

N=AFSPTR( 1,1)

M=AFSPTR( 2,1)

DP=PS(I)+PW(I)+PZ(M)-PZ(N)

IF(DP.GT.O.O) THEN

MCP=CPAIR*FAREA( I )* SQRTDZ (M)*DP**FEXP ( I

)

MCPM(N)=MCPM(N)+MCP

MCPTM(N)=MCPTM(N)+MCP*TZ(M)

ELSE IF(M.GT.O) THEN

MCP=CPAIR* FAREA( I )*SQRTDZ ( N

) *

( -DP ) ** FEXP ( I

)

MCPM(M)=MCPM(M)+MCP

MCPTM(M)=MCPTM(M)+MCP*TZ(N)

END IF

40 CONTINUE

DO 50 N=1 ,NZON

IF(LIST.GE.l) PRINT*, 'MCPM: ' ,N,PZ(N) ,MCPM(N)

50 CONTINUE

C IF (LI ST. GE. 1 ) PRINT FLOWS.

DO 60 1=1 ,NAFS

N=AFSPTR( 1,1)

M=AFSPTR( 2,1)

F=0.0

DP=PS(I)+PW(I)+PZ(M)-PZ(N)

IF(DP.LT.O.O) THEN

F=-FAREA( I

) * SQRTDZ ( N

) *

( -DP ) **FEXP ( I

)

IF(LIST.GE.l) PRINT*, 'FLOW: ' , I ,M, FAREA( I ), SQRTDZ (N) , DP ,

F

ELSE IF(DP.GT.O.O) THEN

F=FAREA( I

) *SORTDZ (M)*DP**FEXP ( I

)

IF(LIST.GE.l) PRINT*, ’FLOW: ’ ,I,M,FAREA(I) , SQRTDZ (M) ,DP,F

END IF

60 CONTINUE

RETURN

END

22
Subroutine SOLVZP computes the room air pressures. It consists of an initialization section (lines 27-54) and an iteration section (lines 56-116).

The initialization is done by computing the room air pressures using flow

exponents of 1. This produces a set of linear equations which are solved by

Gauss elimination (line 50). In TARP , initialization is done only on the

first heat balance iteration of each hour (line 32); otherwise, it is better

to use the most recently computed room pressures. The components of the

Jacobian matrix (AA) and the net room air flows are computed between lines 68

and 95. The test at line 72 prevents division by zero at line 79 and does not

otherwise effect the solution. The test at line 91 accounts for rooms where

the net air flow is too small to effect the room energy requirement and avoids

a possible indefinite result (0/0) at line 92. The primary convergence test

at line 92 compares relative flows. The Newton's method matrix is solved by

gauss elimination at line 96. The TCOUNT variable prevents endless iteration

in case of failure to converge (line 99). The simple improvement for successive

over-corrections is in lines 103 through 106.

Descriptions of local variables:

I index for openings.

N room number

M adjacent room number (0 = ambient).

DP pressure difference across opening (Pa)

F mass flow rate through the opening (kg/s).

DF derivative of the flow rate.

AA Jacobian matrix.

BB sum of air flows into room (kg/s).

CC Newton correction to the room pressures (Pa)

DD Prior iteration corrections (Pa).

123

4 C

5

6

7 C

8

9

10 C

11

12

13 C

14

15

16 C

17

18

19

20 C

21

SUBROUTINE SOLVZP

INTEGER MAXAFS

PARAMETER (MAXAFS=128)

INTEGER MAXZON

PARAMETER (MAXZ0N=36)

COMMON /AFSL/ FAREA(MAXAFS ) ,FEXP(MAXAFS) ,ZS(MAXAFS) ,ZT(MAXAFS)

,

PW( MAXAFS) , PS(MAXAFS) , FAZM( MAXAFS )

, AFSPTR( 2 , MAXAFS)

INTEGER AFSPTR

REAL FAREA, FEXP , ZS, PW, PS, FAZM, ZT

COMMON /ENVT/ ODB ( 1 ) ,0BP( 1 )

, SPD( 1 ) ,DIR( 1 )

, AIRDEN , CPAIR, DTR, STDTIM,

LIST, HCOUNT , ACNVG 1

, ACNVG2 , ACNVG3 , AMAXI T , FRACT , NAFS , NZON

INTEGER STDTIM, HCOUNT, AMAXI T, NAFS, NZON

REAL ODB, OBP , SPD , DIR, AIRDEN, CPAIR, DTR,

ACNVG1 , ACNVG2, ACNVG3 , FRACT

COMMON / ZONL / MCPM( MAXZON )

, MCP TM ( MAXZON )

, TZ ( 0 : MAXZON )

,

23
22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

52

63

64

65

66

67

68

69

70

71

72

ZZ(0:MAXZON) , SQRTDZ(0 rMAXZON) ,PZ(0 :MAXZ0N)

,

FAHS ( MAXZON )

, SUMAF ( MAXZON

)

C

REAL TZ, ZZ, SQRTDZ, PZ, FAHS, MCPM, MCPTM, SUMAF

C

INTEGER TCOUNT

LOGICAL CNVG

REAL AA(MAXZ0N, MAXZON) , BB( MAXZON )

, CC( MAXZON) ,DD(MAXZ0N)

IF(LIST.GE. 1) PRINT *, ' INITIALIZATION ' TC0UNT=0

IF( HCOUNT. EQ. 1 ) GO TO 30

DO 10 N=1 ,NZ0N

DD(N)=1 .

0

BB(N)=FAHS(N)

DO 10 M=1 ,NZON

10 AA(N ,M)=0 .

0

DO 20 1=1 ,NAFS

N=AFSPTR( 1,1)

M=AFSPTR( 2,1)

AA(N,N)=AA(N,N)-FAREA(I)

bb(n)=bb(n)-farea(i)*(ps(i)+pw(i)

)

IF(M.LE.O) GO TO 20

AA(M,M)=AA(M,M)-FAREA(I)

AA(N,M)=AA(N,M)+FAREA( I)

AA(M,N)=AA(M,N)+FAREA(I)

bb(m)=bb(mHfarea(i)*(ps(i)+pw(i))

20 CONTINUE

IF(LIST.GE. 2) CALL DUMPAB ( AA,BB ,NZ0N , MAXZON)

CALL GAUSSY(AA,BB,CC,NZON, MAXZON)

DO 25 N=1 ,NZ0N

PZ(N)=CC(N)

IF(LIST.GE. 1) PRINT*, 'PZ: ',N,PZ(N)

25 CONTINUE

C NEWTON ITERATION.

30 CONTINUE

TCOUNT=TCOUNT+l

IF(LIST.GE. 1 ) PRINT *, 'BEGIN ITERATION ',TCOUNT

CNVG=. FALSE.

DO 40 N=1 ,NZON

BB(N)=FAHS(N)

SUMAF ( N

) =0 .

0

DO 40 M=1 ,NZON

AA(M,N)=0 .

0

40 CONTINUE

C EVALUATE FUNCTIONS AND

C PARTIAL DERIVATIVES.

DO 50 1=1 , NAFS

N=AFSPTR( 1,1)

M=AFSPTR(2,I)

DP=PZ(M)-PZ(N)+PS(I)+PW(I)

IF(ABS(DP) .LT.ACNVG3*

24
73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

(ABS(PZ(M) )+ABS (PZ(N) )+ABS(PS( I ) )+ABS(PW( I ) ) )

)

GO TO 50

IF(DP.LT.O.O) THEN

F=-FAREA(I)*SQRTDZ(N)*(-DP)**FEXP(I)

ELSE

F=FAREA( I

) * SQRTDZ ( M) *DP** FEXP ( I

)

END IF

DF=F*FEXP(I)/DP

BB(N)=BB(N)+F

SUMAF ( N

) = SUMAF ( N ) +AB S ( F

)

AA(N,N)=AA(N,N)-DF

IF(M.LE.O) GO TO 50

BB(M)=BB(M)-F

SUMAF(M)=SUMAF(M)+ABS( F)

AA(M,M)=AA(M,M)-DF

AA(N,M)=AA(N,M)+DF

AA(M,N)=AA(M,N)+DF

50 CONTINUE

DO 60 N=1 ,NZON

IF(ABS(BB(N)) .LE.ACNVG2) GO TO 60

IF(ABS(BB(N)/ SUMAF(N) ) .GT. ACNVG1 ) GO TO 70

60 CONTINUE

CNVG=. TRUE.

70 CONTINUE

IF(LIST.GE. 2) CALL DUMPAB(AA,BB ,NZ0N ,MAXZON)

C CHECK CONVERGENCE.

IF(CNVG) GO TO 999

IF(TCOUNT.GT.AMAXIT) STOP ’ ITERATIONS

C SOLVE AA * CC = BB.

CALL GAUSSY(AA,BB,CC,NZON,MAXZON)

C IMPROVE CONVERGENCE.

DO 80 N=1 ,NZON

IF(CC(N)/DD(N).LE.-0.5) CC(N)=CC(N)*FRACT

IF( ABS( CC(N) ) .GT.ACNVG3) DD(N)=CC(N)

80 CONTINUE

C REVISE PZ.

DO 90 N=1 ,NZON

PZ(N)=PZ(N)-CC(N)

IF(LIST.GE.l) PRINT *, ’REVIS: ' ,N,DD(N) , CC(N) ,PZ(N) ,BB(N)

, SUMAF(N)

90 CONTINUE

GO TO 30

C

999 CONTINUE

PRINT*, ’ITERATIONS ’,TCOUNT

RETURN

END

25
Subroutine GAUSSY is a Gauss elimination routine for computing the correction

terms in Newton's method. The elimination is done in lines 7 through 12.

There is no pivoting because the matrix is diagonally dominant and row exchanges

would never occur. Lines 14 through 18 allow for an indeterminate solution

which occurs if, for example, we are solving for the air flow between two rooms but have no openings from the rooms to ambient. The back substitution

is concluded in lines 19 through 23.

1 SUBROUTINE GAUSSY(A,B,X,N,MAX)

2 C

3 REAL A( MAX, MAX) , B(MAX) , X(MAX)

4 C

5 C

6 C

7

8

9

10

11

12 10

13 C

14

15

16

17

18

19

20

21

22 20

23 30

24 C

25 RETURN

26 END

GAUSS ELIMINATION.

NO PIVOTING.

DO 10 K=1 ,N-1

DO 10 I=K+1,N

D=A(I,K)/A(K,K)

B(I)=B(I)-B(K)*D

DO 10 J=K+1,N

A(I,J)=A(I,J)-A(K,J)*D

BACK SUBSTITUTION.

IF(ABS(A(N,N)).LT.1.E-12) THEN

X(N)=0 .0

ELSE

X(N)=B(N)/A(N,N)

END IF

DO 30 I=N-1 , 1,-1

D=0.

0

DO 20 J=I+1,N

D=D+A( I , J)*X( J)

X(I)=(B(I)-D)/A(I,I)

Subroutine DUMPAB will dump the contents of the Jacobian matrix (A) and the

net room air flows (B) when detailed output has been requested (LIST=2).

12

3

4

56

78

9

SUBROUTINE DUMPAB ( A,B ,N,MAX)

C

REAL A( MAX, MAX) , B(MAX)

C

DO 10 1=1,

N

10 WRITE (* , 101 ) I, (A(I , J) ,J=1 ,N) ,B(I)

101 F0RMAT( 14 , i 1E1 1 . 4

)

RETURN

END

26
APPENDIX B: SAMPLE INPUT FOR THE AIR FLOW TEST PROGRAM

The following sample input deck describes a nine room, single story building

as shown in the plan below. An opening is simulated on every wall. The first

nine lines give the room height, temperature, and system air flow (read at

line 53 of INITAIR) for each room. Room input is terminated at the line with

a negative height. The next 24 lines describe the openings in the envelope

and partition walls (read at line 71 of INITAIR). Each line gives the room

number (room numbers must be sequential from 1), the number of the room on the

opposite side of the wall (0 = ambient), the opening area, the flow exponent,

the flow coefficient, the azimuth angle of the wall, the height of the opening,

and the height of the wall. Openings in partitions are described only once.

The openings information is terminated by the negative room number. The next

line gives the convergence, wind, and output control data (NAMELIST input read

at line 15 of MAIN). Simulation is terminated when the permitted air flow

iterations (AMAXIT) are zero.

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

1.5 20.0 0.0

-1 .0 20. 0.0

1 0 .02 .66 .60 0 . 1.5 3.0

1 0 .02 .66 .60 90. 1.5 3.0

1 2 .16 .50 .60 180. 1.5 3.0

1 4 .16 .50 .60 270. 1 . 5 3.0

2 0 .02 .66 .60 90. 1.5 3.0

2 3 .16 .66 .60 180. 1.5 3.0

2 9 .04 .50 .60 270. 1.5 3.0

3 0 .02 .66 .60 90. 1.5 3.0

3 0 .02 .66 .60 180. 1.5 3.0

3 5 .16 .50 .60 270. 1.5 3.0

4 0 .02 .66 .60 0 . 1.5 3.0

4 9 .04 .50 .60 180. 1 . 5 3.0

4 6 .16 .50 .60 270. 1.5 3.0

5 0 .02 .66 .60 180. 1.5 3.0

5 8 .16 .50 .60 270. 1.5 3.0

5 9 .04 .50 .60 0 . 1.5 3.0

6 0 .02 .66 .60 0. 1.5 3.0

6 7 .16 .50 .60 180. 1.5 3.0

6 0 .02 .66 .60 270. 1.5 3.0

7 9 .04 .50 .60 90. 1.5 3.0

7 8 .16 .50 .60 180. 1.5 3.0

7 0 .02 .66 .60 270. 1.5 3.0

t

N

0

R

T

H

6 4 1

7 9 2

00 5 3

27
8 0 .02 .bb .b0 130. 1.5 3.0

8 0 .02 .66 .60 270. 1.5 3.0

-1 0 .02 .66 .60 270. 4.5 6.0

AMAXIT=20 ,ACNVG1= .01 ,ACNVG2=. 00001 ,ACNVG3=. 00001 ,SPD=5 .000 ,DIR=0

AMAXIT=0 /

. ,LIST=1 /
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 83-2635

2. Performing Organ. Report No. 3. Publication Dace

February 1983

4. TITLE AND SUBTITLE

A Computer Algorithm for Estimating Infiltration and

Inter-Room Air Flows

5. AUTHOR(S)

George N. Walton

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

National Bureau of Standards

U.S. Department of Energy, Building Energy Sciences Branch

Office of Building Energy Research and Development

Washington, DC 20545

10. SUPPLEMENTARY NOTES

~~ ~~~

j Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant in formation. If document includes a significant

bi bl iography or literature survey, mention it here)

This report discusses the extension of an infiltration predicting technique to

the prediction of inter-room air movements. The air flow through openings is

computed from the ASHRAE crack method together with a mass balance in each room. Simultaneous solution of the mass balances in all rooms having both large and

small openings is accomplished by a slightly modified Newton's method. A simple

theory for two-way flow through large openings is developed from consideration

of density differences caused by different temperatures in adjoining rooms. The

technique is verified by comparison to published experimental results. The

results indicate that the simple model provides reasonable results for complex

two way flows through openings. The model is as accurate as the available data,

that is, about +20%. The air flow algorithm allows infiltration and forced air

flows to interact with the doorway flows to provide a more general simulation

capability.

i

12.

KEY WORDS (Six to twelve entries; alphabeti cal order; capitalize only proper names ; and separate key words by semicolons/

Building energy analysis; building heat transfer; computer modeling;

convection; infiltration; ventilation.

13. AVAILABILITY

jjjjJ Unlimited

[ | For Official Distribution. Do Not Release to NTIS

|

| Order From Superintendent of Documents, U.S. Government Printing Office, Washington,

20402.

D.C.

14. NO. OF

PRINTED PAGES :

15. F'ice

XX] Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $8.50

JSCOMM-OC 8043-P 80